Senate Majority Leader Harry Reid said Tuesday that he got a heads up from the White House about the May 31 swap that led to five Taliban detainees being sent to Qatar in exchange for Army Sgt. Bowe Bergdahl.

"As I recall, he was released on Saturday. I got a call from the White House on Friday," the Nevada Democrat said.

The White House has contended the need to act quickly precluded advanced notice given the risks that the deal could fall through and the risks to Bergdahl's life.

Other senior lawmakers on both sides of the aisle didn't get advance notice, but have since gotten calls from the White House.

Senate Intelligence Chairwoman Dianne Feinstein said Tuesday that Deputy National Security Adviser Tony Blinken "apologized" when notifying her about the exchange and said it was an "oversight" not to have notified her earlier.

"In so many words, I can't say, but that was my impression," the California Democrat said.

Senate Minority Leader Mitch McConnell, R-Ky., said he was notified on May 31, but didn't remember whether it was before or after the public release.

Sen. Saxby Chambliss, R-Ga., said he did not get proper notice, either. He said he eventually received an apology from the administration.

"I haven't had a conversation with the White House on this issue in a year and a half," he said. "And if that's keeping us in the loop, then this administration is more arrogant than I thought they were."

Chambliss stressed that he is pleased Bergdahl was released, but noted that issues with the soldier are separate from how the release was handled and conducted.

"I am happy the guy is back, he was a prisoner of war, he’s an American soldier,” Chambliss said. "I am happy for the family. I am father, if that were my son I sure would be glad that he was home, so I am happy for the family in that respect. But that is an entirely different question. If there were negotiations going on, of which the president said he kept Congress ... that is simply not the case."

Senate Armed Services Chairman Carl Levin, D-Mich., said Tuesday that he did not recall hearing of a connection between Bergdahl and the potential release or transfer of the Taliban detainees in any of the recent discussions.

"There was discussion months ago, maybe a year ago, I can't remember when, about the transfer of detainees in order to promote discussions with the Taliban. I thought that would be a mistake," Levin told reporters. "This Bergdahl issue's totally different from that. This is then the question of whether we keep a commitment which we make to our troops that we will do everything we can to get them back.

"I'm saying that Congress was put on notice that the president took the position explicitly when he signed it in Dec. 2013 that he would use his authority if necessary in the area of detainees being transferred," Levin said.

Levin demurred when asked if he thought Obama had the authority he claimed in the signing statement accompanying the defense programs bill to not provide the proper notice under the circumstances.

"I'm not going to reach a legal conclusion. All I can tell you is that all presidents have asserted their authority under the second article of the constitution as commander-in-chief, including under the War Powers Act," Levin said.

"I've been told no, he did not violate the law," Reid said in a response to a question about a 30-day statutory notification requirement.

Feinstein said she had questions about whether Bergdahl was a deserter and the terms of Qatar taking the prisoners from Guantánamo Bay and others. She said that the president "has an executive authority he can use."

Reid said that White House Chief of Staff Denis McDonough appeared at the weekly Democratic lunch "to explain the situation with Bergdahl."

On the broader issue of closing the detention facility, Reid expressed hope that would move forward.

"In my own personal opinion, Guantánamo has been there far too long, and I think we should get them out of there as quick as we can. We've been held up from doing that by the Republicans not wanting them, any of them to be tried here in the United States," Reid said. "I'm glad to get rid of these five people and send them back to Qatar."